Primary Analyses for Experiments 1-3, not excluding influential participants
Across all of our experiments, we checked for influential participants in every model we fit, as stated in the main text. This is a way of detecting outliers, or individuals whose inclusion in the analysis might have undue influence by either masking the effect, which is otherwise present across the rest of the sample, or by driving the effect, which is otherwise absent across the rest of the sample. We did not find any influential observations in the primary analyses in Experiments 4 and 5, but did detect some in Experiments 1 through 3.
Experiment 1
In the primary analysis for Experiment 1, we detected one influential participant. Including them in the sample generates the same finding as reported in the main text: Infants looked equally at the efficient vs inefficient reach of a mittened hand ([-0.169,0.209], ß=0.041, B=0.02, SE=0.092, p=0.831, two-tailed).
Experiment 2
In the primary analysis for Experiment 2, we detected 2 influential participants. Including them in the sample generates a marginal effect in the same direction as that reported in the main text: Infants looked longer at the inefficient than the efficient reach of a bare hand ([-0.024,0.318], ß=0.297, B=0.147, SE=0.083, p=0.091, two-tailed). As stated in the main text, our overall conclusion from Experiments 1 and 2 is that infants have inconsistent, fragile expectations about the efficiency of reaches that result in displacing objects.
Experiment 3
In the primary analysis for Experiment 3, we detected 2 influential participants. Including them in the sample generates the same finding as reported in the main text: Infants’ looking preferences for the test events differed as a function of whether they were habituated to constrained action over a barrier (experimental group) or the same actions not over a barrier (control group) ([0.115,0.657], ß=0.596, B=0.502, SE=0.114, p<.001, two-tailed). In the experimental condition, infants looked longer at the inefficient action ([0.065,0.451], ß=0.398, B=0.258, SE=0.095, p=0.01, two-tailed). In the control condition, infants looked equally at the two test actions ([-0.321,0.065], ß=-0.198, B=-0.128, SE=0.095, p=0.186, two-tailed).
Comparing Experiments 1-2 with Skerry et al. (2013)
We compared the results of Experiment 4 and 5 against those from Skerry et al’s Experiment 3, wherein infants received no mittens training and viewed a person reaching with a mittened hand. The results of Experiment 5 (no mitten) differed from those of the earlier experiment (mitten), [-0.547,-0.047], ß=-0.539, B=-0.297, SE=0.124, p=0.022, two-tailed, mixed effects model with fixed interaction between experiment and test event and random intercept for participants, one influential participant excluded on the basis of Cook’s Distance. In addition, the results from Experiment 4 (mitten) marginally differed from those in of Skerry et al. (mitten), [-0.464,0.015], ß=-0.43, B=-0.224, SE=0.122, p=0.074, two-tailed, mixed effects model with fixed interaction between experiment and test events and random intercept for participants, 2 influential participants excluded on the basis of Cook’s Distance.
Meta-analytic results
To assess the unique effects of our experimental manipulations in Experiments 1-5 and in Skerry et al. (28), we performed an analysis over these two papers (total N=264, 12 conditions). Our analytic approach allows us to assess the independent effects of 5 manipulations: the type of or absence of motor training, the presence or absence of barrier preventing a direct reach for the object during habituation, the nature of the goal (to change the state of an object or pick it up), the presence or absence of action on contact, and the presence of absence of mittens on the actor. The analysis also allows us to control for the participant variables age and sex, and model the nested structure of the data (e.g. looks clustered within experiments and within papers). For ease of interpretation, we used average proportion looking to the inefficient action in this analysis, following Skerry et al. (28)).
This analysis confirmed the findings from the individual experiments reported in the main text and in Skerry et al. (28): Infants’ expectations were stronger when the observed action was spatiotemporally continuous with its effect (i.e., appeared to be causal), [0.027,0.06], ß=0.505, B=0.045, SE=0.009, p<.001, two-tailed, when infants received effective motor training (sticky mittens), relative to no training [0.027,0.069], ß=0.545, B=0.048, SE=0.012, p=0.004, two-tailed, when the observed agent’s actions were constrained by a barrier and were efficiently adapted to that barrier, relative to the same actions that were unconstrained by a barrier, [0.021,0.051], ß=0.407, B=0.036, SE=0.008, p=0.001, two-tailed, and when the agent pursued a state change goal, relative to a pickup goal, [0.02,0.053], ß=0.416, B=0.037, SE=0.009, p=0.009, two-tailed. We also found that infants’ expectations were marginally negatively affected when they received ineffective motor training (non-sticky mittens), relative to no training, [-0.06,-0.005], ß=-0.366, B=-0.032, SE=0.015, p=0.063, two-tailed, and were unaffected when the actor wore a mitten, relative to no mitten [-0.045,0], ß=-0.25, B=-0.022, SE=0.012, p=0.111, two-tailed, as reported in the main text. These findings provide further evidence that action experience alters action interpretation, for good or for ill, but so does causal information and information about efficiency.

Figure S1. Looking time in seconds towards the efficient versus inefficient reach (bottom), and proportion looking towards the inefficient reach (top) at test across Experiments 1-5 (n=152) and across Experiments 1-5 in Skerry et al. (SCS)32 (n=112). Labels above each panel list the experiment name (Exp. 1-5, SCS Exp. 1-5), type of motor training (none, ineffective non-sticky mittens, or effective sticky mittens), whether actions during habituation were constrained or unconstrained by a barrier, goal (state.change or pick.up), whether actions resulted in contact with the object, whether the actor wore a mitten, and video displays listed in Figure 1. Error bars around means indicate within-subjects 95% confidence intervals (bottom) and bootstrapped 95% confidence intervals (top). Individual points (top) or pairs of connected points (bottom) indicate data from a single participant. Horizontal bars within boxes indicate medians, and boxes indicate the middle 2 quartiles of data. Violin plots (top) indicate distribution of data, area scaled proportionally to the number of observations.

Figure S2. Effect plots for model investigating predictors of sensitivity to action efficiency across Experiments 1-5 and Skerry et al. (2013) 32 (total N=264, 247 included in final analysis, 17 excluded on the basis of Cook’s Distance). Each point shows estimates of effects at each level of all categorical predictors: Type of motor training (none, ineffective non-sticky mittens, or effective sticky mittens), the goal of the actor (state change vs pick up), action during habituation (constrained or unconstrained by a barrier), whether actions resulted in contact with the object (yes or no), whether the actor wore a mitten (yes or no). Error bars indicate 95% confidence intervals. See Table S1 for full results.
Table S1. Regression table for model investigating predictors of sensitivity to action efficiency across Experiment 1-5 and all experiments from Skerry et al. (total N=264, 247 included in final analysis, 17 excluded on the basis of Cook’s Distance). Dependent measure is proportion looking towards the inefficient reach, averaged across 3 test trials during test. Categorical predictors were coded using sum contrasts, and fixed effects from the model should therefore be interpreted with respect to the grand mean (with respect to 0). Model formula: prop.ineff.all ~ training + goal + hab + causal + mitten + (1|experiment) + (1|ageday) + (1|sex) + (1|paper).
| (Intercept) |
-0.331 |
0.489 |
0.018 |
8.35 |
26.86 |
0.000 |
0.457 |
0.523 |
| effective training |
0.545 |
0.048 |
0.012 |
7.04 |
4.20 |
0.004 |
0.027 |
0.069 |
| ineffective training |
-0.366 |
-0.032 |
0.015 |
8.49 |
-2.13 |
0.063 |
-0.060 |
-0.005 |
| state change goal |
0.416 |
0.037 |
0.009 |
5.50 |
3.96 |
0.009 |
0.020 |
0.053 |
| constrained habituation |
0.407 |
0.036 |
0.008 |
11.16 |
4.47 |
0.001 |
0.021 |
0.051 |
| causally effective |
0.505 |
0.045 |
0.009 |
24.41 |
5.06 |
0.000 |
0.027 |
0.060 |
| mitten |
-0.250 |
-0.022 |
0.012 |
7.72 |
-1.80 |
0.111 |
-0.045 |
0.000 |
This analysis confirmed that first-person action experience is not the only way to enhance infants’ appreciation of the causal and intentional aspects of action. It also confirmed the findings from the individual experiments reported in the main text and from Skerry et al. (2013): Infants’ expectations were stronger when the observed action was spatiotemporally continuous with its effect (i.e., appeared to be causal),[0.027,0.06], ß=0.505, B=0.045, SE=0.009, p<.001, two-tailed, when infants received effective motor training (sticky mittens), relative to no training, [0.027,0.069], ß=0.545, B=0.048, SE=0.012, p=0.004, two-tailed, when the observed agent’s actions were constrained by a barrier and were efficiently adapted to that barrier, relative to the same actions that were unconstrained by a barrier, [0.021,0.051], ß=0.407, B=0.036, SE=0.008, p=0.001, two-tailed, and when the agent pursued a state change goal, relative to a pickup goal, [0.02,0.053], ß=0.416, B=0.037, SE=0.009, p=0.009, two-tailed. We also found that infants’ expectations were marginally negatively affected when they received ineffective motor training (non-sticky mittens), relative to no training, [-0.06,-0.005], ß=-0.366, B=-0.032, SE=0.015, p=0.063, two-tailed, and were unaffected when the actor wore a mitten, relative to no mitten [-0.045,0], ß=-0.25, B=-0.022, SE=0.012, p=0.111, two-tailed, as reported in the main text.
Attention during habituation across Exp 1-5

Figure S4. Total looking time in seconds during habituation across Experiment 1-5. Error bars around means indicate bootstrapped 95% confidence intervals (CIs). Individual points indicate data from a single participant. Horizontal bars within boxes indicate medians, and boxes indicate the middle 2 quartiles of data. Violin plots in indicate distribution of data, area scaled proportionally to the number of observations.

Figure S5. Looking time in seconds during each habituation trial across Experiments 1-5. Curves with 95% confidence interval ribbons indicate smoothed conditional means, generated using the loess method. Connected points indicate data from a single participant. Labels above each panel list the experiment name (Exp. 1-5), whether actions during habituation were constrained or unconstrained by a barrier, goal (state.change or pick.up), whether actions resulted in contact with the object, whether the actor wore a mitten, and video displays listed in Figure 1.
Table S3 Regression table for mixed effects model analyzing the effect of age, sex, order of test events, habituation condition, goal, mitten, and causal information on total attention during habituation, controlling for variations across Experiments 1-5. Model formula: total_hab ~ ageday + sex + first.test + hab + goal + mitten + causal + (1|experiment)
| (Intercept) |
-0.208 |
343.171 |
76.54 |
151.78 |
4.483 |
0.000 |
192.19 |
494.168 |
| Age in Days |
-0.233 |
-2.058 |
0.68 |
147.54 |
-3.026 |
0.003 |
-3.40 |
-0.714 |
| Sex |
0.066 |
5.203 |
6.11 |
148.65 |
0.852 |
0.396 |
-6.92 |
17.274 |
| First Test Event |
-0.006 |
-0.439 |
6.00 |
146.65 |
-0.073 |
0.942 |
-12.27 |
11.393 |
| Habituation |
0.222 |
17.590 |
11.03 |
131.57 |
1.595 |
0.113 |
-6.44 |
41.220 |
| Goal |
0.007 |
0.589 |
16.02 |
6.18 |
0.037 |
0.972 |
-37.44 |
37.615 |
| Mitten |
0.126 |
9.996 |
19.02 |
5.73 |
0.525 |
0.619 |
-35.14 |
55.088 |
| Causal |
-0.055 |
-4.379 |
9.08 |
75.38 |
-0.482 |
0.631 |
-23.75 |
13.935 |
To ask whether infants’ total attention during habituation was affected by experimental manipulations across Experiment 1-5 (action constrained vs unconstrained by a barrier, state change vs pickup goal, mitten vs no mitten on actor, and action with vs without contact with the object), and varied by gender and age, we fit a mixed effects model on these fixed effects and experiment (Exp.1-5) as a random intercept. We found that the only robust predictor of attention during habituation was age, [-3.4,-0.714], ß=-0.233, B=-2.058, SE=0.68, p=0.003, two-tailed, such that older infants looked for a shorter time overall than younger infants.